As for KLD, have you tried it on something which is even closer to e2e task, like agentic traces from https://huggingface.co/datasets/nvidia/Nemotron-Cascade-2-SF... or similar datasets?
If you would like to do so, it is easy (and orders of magnitude cheaper) than running benchmarks.
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As for KLD, have you tried it on something which is even closer to e2e task, like agentic traces from https://huggingface.co/datasets/nvidia/Nemotron-Cascade-2-SF... or similar datasets?